Question: Solve for $x$ : $9\sqrt{x} + 7 = 6\sqrt{x} + 5$
Answer: Subtract $6\sqrt{x}$ from both sides: $(9\sqrt{x} + 7) - 6\sqrt{x} = (6\sqrt{x} + 5) - 6\sqrt{x}$ $3\sqrt{x} + 7 = 5$ Subtract $7$ from both sides: $(3\sqrt{x} + 7) - 7 = 5 - 7$ $3\sqrt{x} = -2$ Divide both sides by $3$ $\frac{3\sqrt{x}}{3} = \frac{-2}{3}$ Simplify. $\sqrt{x} = -\dfrac{2}{3}$ The principal root of a number cannot be negative. So, there is no solution.